Abstract: In this paper, we will find the orthogonal projected length or area of some figures.
Especially it will show the simplest way to find the orthogonal projected area of ellipsoid. And
then we apply them to the problem “Run or walk in the rain?” We will consider that the objects
move in the rain in a given time as well as in a given distance. And we also take into account an
object which moves leaning its body. By a simple method in this paper, we can check the
conclusions the previous authors pointed out. Furthermore we can obtain the new formulas and
results. So I think, at least in theory, this paper will show the way to reach the final conclusion
about this problem.​

Background see the author's original thread.
I don't know what to think about the journal ... a pdf of the paper is attached to the linked thread.
Is that typical of the sort of thing they publish?

The author basically works out the volume that various primitives (rectangular prism, spheroid, cylinder) sweep out and multiplies this by the number density of raindrops ... the whole thing looks like it's done in the reference frame of the ground.

I think the conclusion is that running is better than walking, provided you run at the right angle to the rain. This appears to contradict simple experiments conducted using natural running vs walking in simulated in-Nature weather.

Real running is very different from models. Mythbusters took a crack at this once, and you can see from how they went about it that there are a lot of factors going into it.

But if we do take a model where a solid body simply moves through a field of rain drops (rain's frame of reference is far more convenient here) is there any surprise that moving faster gets the object less wet? A plane parallel to rainfall is going to seep out exactly the same area regardless. A plane orthogonal rain fall is going to pick up very little if it moves fast enough. An arbitrary body will trivially fall somewhere in between, with a slight advantage for a fast moving object.

But an actual running person is going to splash, bob, and go through a different sequence of poses than a walking person. Comparing such a simplistic model to an experiment with an actual person is absolutely pointless.

The model may be better applied to a planetoid moving through a debris field ... except: no gravity in the model.
I was surprised that it got published - then I find out that it is "pre-review". <sigh>

I believe the author would do better to remove the human and weather elements of the paper, and reduce the problem to a set of variables that can be accounted for and controlled. Or at least try to account for them to a higher degree, right now the paper fails at drawing his conclusion.

Has it occurred to anyone that if walking speed is half of running speed, one would be exposed to the rain for twice the time when walking? It's a fairly simple proposition regardless of the angle of the rainfall and the direction that the person might take.